Within this chapter developmental plasticity was explored within Acanthochromis polyacanthus that were collected from two different regions (i.e., low-latitude, Cairns, and high-latitude, Mackay). Fish were held in common garden experiments at 28.5 C. Clutch data was collected along with parental morphometeric data to determine how fish from each population performed at 28.5 C, a temperature that was shown to produce similar absoluate aerobic scope performances in a previous study [link]. Once hatched offspring were placed into three different temperature treatments, 28.5, 30, and 31.5 C. After approximately 5-6 months offspring length and weight was measured, as well as CTmax and respiration during CTmax trials.
library(tidyverse) # data manipulation
library(ggpubr) # figure arrangement
library(brms) # Bayesian models
library(StanHeaders)# needed to run Bayesian models
library(rstan) # needed to run Bayesian models
library(standist) # needs to be installed
library(bayesplot) # needed for MCMC diagnostics
library(DHARMa) # model validation
library(ggdist) # partial plots
library(tidybayes) # partial plots
library(broom.mixed) # model investigation
library(emmeans) # pairwise comparisons
library(rstanarm) # pairwise comparisons - need for emmeans
library(car) # for vif
library(modelsummary) # descriptive statisticsgrowth <- read_delim("./import_files/growth_data.txt",
delim = "\t", escape_double = FALSE,
col_types = cols(NOTES = col_skip(),
...16 = col_skip(), ...17 = col_skip()),
trim_ws = TRUE)
clutch_data <- read_delim("import_files/clutch_data_2022_2023.txt",
delim = "\t", escape_double = FALSE,
trim_ws = TRUE) %>%
mutate(CLUTCH_NUMBER = as.factor(CLUTCH_NUMBER))density <- count(growth, CLUTCH_NUMBER, TANK) |>
rename(DENSITY = n) |>
mutate(CLUTCH_NUMBER = as.factor(CLUTCH_NUMBER),
TANK = as.factor(TANK))
growth2 <- growth |>
mutate(CLUTCH_NUMBER = as.factor(CLUTCH_NUMBER),
MALE = as.factor(MALE),
FEMALE = as.factor(FEMALE),
REGION = as.factor(REGION),
POPULATION = as.factor(POPULATION),
DATE_OF_HATCH = as.Date(DATE_OF_HATCH, format = "%d/%m/%Y"),
DATE_SAMPLED = as.Date(DATE_SAMPLED, format = "%d/%m/%Y"),
DEV_TEMP = as.factor(DEV_TEMP),
TANK = as.factor(TANK),
REP = as.factor(REP),
LENGTH = as.numeric(LENGTH),
MASS = as.numeric(MASS),
FULTONK = (1000*MASS)/(LENGTH^3), # Adding FULTON'S K metric
EXPERIMENT = as.factor(EXPERIMENT)) |>
full_join(select(clutch_data, c("CLUTCH_NUMBER",
"MALE_STANDARD_LENGTH",
"MALE_MASS",
"MALE_LAT",
"MALE_LONG",
"FEMALE_STANDARD_LENGTH",
"FEMALE_MASS",
"FEMALE_LAT",
"FEMALE_LONG",
"CLUTCH_ORDER",
"DAYS_IN_TREATMENT",
"EGG_COUNT",
"HATCHING_SUCCESS")), by = "CLUTCH_NUMBER") |>
select(c(1:6,16:27,7:13,15,14)) |>
drop_na(EXPERIMENT) |>
mutate(CLUTCH_ORDER = as.factor(CLUTCH_ORDER),
EXP_GROUP = as.factor(paste0(REGION,"_",DEV_TEMP))) |>
inner_join(density, by=c("CLUTCH_NUMBER","TANK")) |>
mutate(FEMALE_MASS = coalesce(FEMALE_MASS, MALE_MASS),
TANK =as.numeric(as.character(TANK)),
LEVEL = as.factor(case_when(TANK >= 1 & TANK <= 199 ~ 1,
TANK >= 200 & TANK <= 299 ~ 2,
TANK >= 300 & TANK <= 399 ~ 3,
TRUE ~ NA_real_))) |>
mutate(TANK = as.factor(TANK)) |>
filter(MASS < 4, na.rm=TRUE,
FULTONK < 0.079,
FULTONK > 0.01,
DENSITY > 3) In the code above a number of variables were centered because within these metrics the value 0 is meaningless. For example you cannot have a fish length or mass of 0. Therefore, the mean was subtracted for a given variable was subtracted by every value. The y-intercept for these values will therefore reflect the mean, and the slope can be interpreted as ‘y increases/decreases x amount for every 1-unit increase from the mean [INSERT METRIC]’.
NOTE: On some of the figures ylimits have been set and therefore outliers are hidden
male.mass.plot <- ggplot(growth2, aes(x=MALE_MASS, y=MASS)) +
geom_point(alpha = 0.5) +
ggtitle("Farther vs. offspring mass") +
theme_classic()
female.mass.plot <- ggplot(growth2, aes(x=FEMALE_MASS, y=MASS)) +
geom_point(alpha = 0.5) +
ggtitle("Mother vs. offspring mass") +
theme_classic()
male.length.plot <- ggplot(growth2, aes(x=MALE_STANDARD_LENGTH, y=LENGTH)) +
geom_point(alpha = 0.5) +
ggtitle("Farther vs. offspring length") +
theme_classic()
female.length.plot <- ggplot(growth2, aes(x=FEMALE_STANDARD_LENGTH, y=LENGTH)) +
geom_point(alpha = 0.5) +
ggtitle("Mother vs. offspring length") +
theme_classic()
ggarrange(male.mass.plot, female.mass.plot, male.length.plot, female.length.plot,
ncol=2,
nrow=2)
## Female Mass
There seems to be three areas that standout as potentially possessing outliers:
Individuals identified in numbered points one and two are not unexpected. These data points will be double check to ensure they were entered correctly, if so they will be removed from the data set.
It looks like there are some issues with the model. Mainly around the presence of outliers. Some of these outliers could be seen in our explanatory data analysis. Let’s revisit our raw data to check and remove the presence of outliers.
MinMax <- function(x) paste0('[', min(x, na.rm = TRUE), ', ', max(x, na.rm = TRUE), ']')
Range <- function(x) max(x, na.rm = TRUE) - min(x, na.rm = TRUE)
datasummary(REGION*(LENGTH + MASS) + (LENGTH + MASS) ~ median + MinMax + Range + Histogram,
data=growth3)| REGION | median | MinMax | Range | Histogram | |
|---|---|---|---|---|---|
| core | LENGTH | 31.47 | [15.15, 46.82] | 31.67 | ▁▃▆▇▄▁ |
| MASS | 1.09 | [0.0882, 3.106] | 3.02 | ▁▃▇▇▅▂▁ | |
| leading | LENGTH | 31.35 | [16.16, 45.17] | 29.01 | ▁▃▆▇▅▂ |
| MASS | 1.07 | [0.138, 3.528] | 3.39 | ▁▄▇▅▃▁ | |
| LENGTH | 31.45 | [15.15, 46.82] | 31.67 | ▁▃▆▇▄▁ | |
| MASS | 1.08 | [0.0882, 3.528] | 3.44 | ▁▃▇▅▃▁ |
datasummary(REGION * DEV_TEMP * (LENGTH + MASS) + (LENGTH + MASS) ~ median + MinMax + Range + Histogram,
data=growth3)| REGION | DEV_TEMP | median | MinMax | Range | Histogram | |
|---|---|---|---|---|---|---|
| core | 28.5 | LENGTH | 32.30 | [16.9, 45.09] | 28.19 | ▁▂▄▇▄▂ |
| MASS | 1.17 | [0.1226, 3.106] | 2.98 | ▂▅▇▅▂▁ | ||
| 30 | LENGTH | 31.29 | [16.15, 46.82] | 30.67 | ▁▃▇▇▂▁ | |
| MASS | 1.07 | [0.1778, 2.7827] | 2.60 | ▁▂▇▇▅▃▁ | ||
| 31.5 | LENGTH | 30.42 | [15.15, 40.03] | 24.88 | ▁▂▄▆▇▅▃▁ | |
| MASS | 1.02 | [0.0882, 2.79] | 2.70 | ▁▅▇▇▅▃▂▁▁▁ | ||
| leading | 28.5 | LENGTH | 31.95 | [16.16, 45.17] | 29.01 | ▁▂▆▇▅▂ |
| MASS | 1.09 | [0.138, 3.06] | 2.92 | ▁▃▇▆▅▃ | ||
| 30 | LENGTH | 32.35 | [16.43, 42.88] | 26.45 | ▁▁▄▆▇▄▁ | |
| MASS | 1.16 | [0.3081, 2.6554] | 2.35 | ▁▄▇▇▇▅▂▁ | ||
| 31.5 | LENGTH | 30.01 | [17.98, 42.35] | 24.37 | ▁▃▇▅▄▁▁ | |
| MASS | 0.97 | [0.1854, 3.528] | 3.34 | ▁▅▇▃▁ | ||
| LENGTH | 31.45 | [15.15, 46.82] | 31.67 | ▁▃▆▇▄▁ | ||
| MASS | 1.08 | [0.0882, 3.528] | 3.44 | ▁▃▇▅▃▁ |
note this also removes NA’s therefore the difference in data frames is 21 row:
Now Let’s look at out plots again
First we will place random factors only within out model and see if they do a good job explaining the variance within our model. We will also be include priors which will be based off of out length data.
Hypothesis test will include:
## `summarise()` has grouped output by 'REGION'. You can override using the
## `.groups` argument.
f.model.null <- bf(MASS ~ 1,
family = gaussian())
model.null <- brm(f.model.null,
data = growth3,
prior = mass.priors.re,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
save_pars = save_pars(all=TRUE),
sample_prior = "yes",
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
f.model1 <- bf(MASS ~ 1 + (1|FEMALE) + (1|TANK),
family=gaussian())
model1 <- brm(f.model1,
data = growth3,
prior = mass.priors.re,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
save_pars = save_pars(all=TRUE),
sample_prior = "yes",
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
f.model2 <- bf(MASS ~ 1 + (1|FEMALE) + (1|TANK) + (1| LEVEL),
family=gaussian())
model2 <- brm(f.model2,
data = growth3,
prior = mass.priors.re,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
save_pars = save_pars(all=TRUE),
sample_prior = "yes",
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
## Warning: There were 23 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
f.model3 <- bf(MASS ~ 1 + (1| FEMALE) + (1| TANK) + (1|LEVEL) + (1| POPULATION),
family=gaussian())
model3 <- brm(f.model3,
data = growth3,
prior = mass.priors.re,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
save_pars = save_pars(all=TRUE),
sample_prior = "yes",
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
## Warning: There were 26 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
f.model4 <- bf(MASS ~ 1 + (1|FEMALE) + (1 |TANK) + (1| LEVEL) + (1| POPULATION)+ (1|CLUTCH_ORDER),
family=gaussian())
model4 <- brm(f.model4,
data = growth3,
prior = mass.priors.re,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
save_pars = save_pars(all=TRUE),
sample_prior = "yes",
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
## Warning: There were 21 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: There were 24 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: Found 1 observations with a pareto_k > 0.7 in model 'model2'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.
## Output of model 'model.null':
##
## Computed from 1800 by 1961 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -1193.5 41.0
## p_loo 2.7 0.3
## looic 2387.0 82.0
## ------
## MCSE of elpd_loo is 0.0.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.9, 1.0]).
##
## All Pareto k estimates are good (k < 0.69).
## See help('pareto-k-diagnostic') for details.
##
## Output of model 'model1':
##
## Computed from 1800 by 1961 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -940.0 42.3
## p_loo 101.0 5.1
## looic 1880.1 84.6
## ------
## MCSE of elpd_loo is 0.3.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.8, 1.1]).
##
## All Pareto k estimates are good (k < 0.69).
## See help('pareto-k-diagnostic') for details.
##
## Output of model 'model2':
##
## Computed from 1800 by 1961 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -940.1 42.3
## p_loo 100.6 5.1
## looic 1880.2 84.7
## ------
## MCSE of elpd_loo is NA.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.3, 1.1]).
##
## Pareto k diagnostic values:
## Count Pct. Min. ESS
## (-Inf, 0.69] (good) 1960 99.9% 270
## (0.69, 1] (bad) 1 0.1% <NA>
## (1, Inf) (very bad) 0 0.0% <NA>
## See help('pareto-k-diagnostic') for details.
##
## Output of model 'model3':
##
## Computed from 1800 by 1961 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -939.1 42.3
## p_loo 99.4 5.0
## looic 1878.2 84.5
## ------
## MCSE of elpd_loo is 0.3.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.1, 1.1]).
##
## All Pareto k estimates are good (k < 0.69).
## See help('pareto-k-diagnostic') for details.
##
## Output of model 'model4':
##
## Computed from 1800 by 1961 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -939.2 42.4
## p_loo 98.9 5.1
## looic 1878.5 84.8
## ------
## MCSE of elpd_loo is 0.3.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.7, 1.2]).
##
## All Pareto k estimates are good (k < 0.69).
## See help('pareto-k-diagnostic') for details.
##
## Model comparisons:
## elpd_diff se_diff
## model3 0.0 0.0
## model4 -0.1 1.1
## model1 -0.9 1.1
## model2 -1.0 0.8
## model.null -254.4 25.9
CLUTCH_ORDER does not improve the model. Therefore it will not be used moving forward.
col.lm <- lm(MASS ~ 1 + DEV_TEMP+REGION +
scale(FEMALE_MASS, center=TRUE, scale=TRUE) +
scale(DENSITY, center=TRUE, scale=TRUE) +
scale(AGE_DAYS, center=TRUE, scale=TRUE) +
scale(LENGTH, center=TRUE, scale=TRUE),
data = growth3)
vif(col.lm)## GVIF Df GVIF^(1/(2*Df))
## DEV_TEMP 1.053304 2 1.013068
## REGION 1.165551 1 1.079607
## scale(FEMALE_MASS, center = TRUE, scale = TRUE) 1.098656 1 1.048168
## scale(DENSITY, center = TRUE, scale = TRUE) 1.119457 1 1.058044
## scale(AGE_DAYS, center = TRUE, scale = TRUE) 1.219351 1 1.104242
## scale(LENGTH, center = TRUE, scale = TRUE) 1.142628 1 1.068938
## `summarise()` has grouped output by 'REGION'. You can override using the
## `.groups` argument.
f.model3.1 <- bf(MASS ~ 1 +
DEV_TEMP*REGION +
scale(DENSITY, center=TRUE, scale=TRUE) +
#scale(AGE_DAYS, center=TRUE, scale=TRUE) +
scale(LENGTH, center=TRUE, scale=TRUE) +
(1| FEMALE) + (1| TANK) + (1|LEVEL) + (1| POPULATION),
family=gaussian())
model3.1 <- brm(f.model3.1,
data = growth3,
prior = mass.priors,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
save_pars = save_pars(all=TRUE),
sample_prior = "yes",
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
## Warning: There were 10 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
## Using 10 posterior draws for ppc type 'dens_overlay' by default.
#--- DHARMa checks ---#
preds <- posterior_predict(model3.1, ndraws=250, summary=FALSE)
model3.1_resids <- createDHARMa(simulatedResponse = t(preds),
observedResponse = growth3$MASS,
fittedPredictedResponse = apply(preds, 2, mean),
integerResponse = 'student')
plot(model3.1_resids) ; testDispersion(model3.1_resids)##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 0.90702, p-value = 0.04
## alternative hypothesis: two.sided
## 'pars' not specified. Showing first 10 parameters by default.
## 'pars' not specified. Showing first 10 parameters by default.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## 'pars' not specified. Showing first 10 parameters by default.
f.model3.2 <- bf(MASS ~ 1 +
DEV_TEMP*REGION +
scale(DENSITY, center=TRUE, scale=TRUE) +
#scale(AGE_DAYS, center=TRUE, scale=TRUE) +
poly(scale(LENGTH, center=TRUE, scale=TRUE), 2) +
(1| FEMALE) + (1| TANK) + (1|LEVEL) + (1| POPULATION),
family=gaussian())
model3.2 <- brm(f.model3.2,
data = growth3,
prior = mass.priors,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
save_pars = save_pars(all=TRUE),
sample_prior = "yes",
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
## Warning: There were 11 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: There were 39 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: Examine the pairs() plot to diagnose sampling problems
## Using 10 posterior draws for ppc type 'dens_overlay' by default.
#--- DHARMa checks ---#
preds <- posterior_predict(model3.2, ndraws=250, summary=FALSE)
model3.2_resids <- createDHARMa(simulatedResponse = t(preds),
observedResponse = growth3$MASS,
fittedPredictedResponse = apply(preds, 2, mean),
integerResponse = 'student')
plot(model3.2_resids) ; testDispersion(model3.2_resids)##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 0.91398, p-value = 0.072
## alternative hypothesis: two.sided
## 'pars' not specified. Showing first 10 parameters by default.
## 'pars' not specified. Showing first 10 parameters by default.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## 'pars' not specified. Showing first 10 parameters by default.
## Warning: Found 1 observations with a pareto_k > 0.7 in model 'model3.1'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.
## Warning: Found 1 observations with a pareto_k > 0.7 in model 'model3.2'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.
## Output of model 'model3.1':
##
## Computed from 1800 by 1961 log-likelihood matrix.
##
## Estimate SE
## elpd_loo 481.3 57.4
## p_loo 106.6 6.9
## looic -962.5 114.8
## ------
## MCSE of elpd_loo is NA.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.7, 1.1]).
##
## Pareto k diagnostic values:
## Count Pct. Min. ESS
## (-Inf, 0.69] (good) 1960 99.9% 207
## (0.69, 1] (bad) 1 0.1% <NA>
## (1, Inf) (very bad) 0 0.0% <NA>
## See help('pareto-k-diagnostic') for details.
##
## Output of model 'model3.2':
##
## Computed from 1800 by 1961 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -324.2 45.1
## p_loo 101.3 5.6
## looic 648.5 90.3
## ------
## MCSE of elpd_loo is NA.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.7, 1.1]).
##
## Pareto k diagnostic values:
## Count Pct. Min. ESS
## (-Inf, 0.69] (good) 1960 99.9% 290
## (0.69, 1] (bad) 1 0.1% <NA>
## (1, Inf) (very bad) 0 0.0% <NA>
## See help('pareto-k-diagnostic') for details.
##
## Model comparisons:
## elpd_diff se_diff
## model3.1 0.0 0.0
## model3.2 -805.5 48.0
There are issues with this model lets fit it using a Gamma distribution.
Note: The Gamma distribution will have a log link function.
model_gamma.priors <- prior(normal(1.13, 0.20), class="Intercept") +
prior(normal(0, 0.25), class="b")f.model3.1_gamma1 <- bf(MASS ~ 1 +
DEV_TEMP*REGION +
scale(DENSITY, center=TRUE, scale=TRUE) +
#scale(AGE_DAYS, center=TRUE, scale=TRUE) +
scale(LENGTH, center=TRUE, scale=TRUE) +
(1| FEMALE) + (1| TANK) + (1|LEVEL) + (1| POPULATION),
family=Gamma(link = "log"))
model3.1_gamma1 <- brm(f.model3.1_gamma1,
data = growth3,
prior = model_gamma.priors,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
sample_prior = "yes",
save_pars = save_pars(all=TRUE),
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
## Warning: There were 4 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: There were 904 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: Examine the pairs() plot to diagnose sampling problems
## Using 10 posterior draws for ppc type 'dens_overlay' by default.
#--- DHARMa checks ---#
preds <- posterior_predict(model3.1_gamma1, ndraws=250, summary=FALSE)
model3.1_gamma1_resids <- createDHARMa(simulatedResponse = t(preds),
observedResponse = growth3$MASS,
fittedPredictedResponse = apply(preds, 2, mean),
integerResponse = 'student')
plot(model3.1_gamma1_resids) ; testDispersion(model3.1_gamma1_resids); testDispersion(model3.1_gamma1_resids, plot = F, alternative = "greater")##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.1673, p-value < 2.2e-16
## alternative hypothesis: two.sided
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.1673, p-value < 2.2e-16
## alternative hypothesis: greater
## 'pars' not specified. Showing first 10 parameters by default.
## 'pars' not specified. Showing first 10 parameters by default.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## 'pars' not specified. Showing first 10 parameters by default.
## Warning: There were 4 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gamma
## Links: mu = log; shape = identity
## Formula: MASS ~ 1 + DEV_TEMP * REGION + scale(DENSITY, center = TRUE, scale = TRUE) + scale(LENGTH, center = TRUE, scale = TRUE) + (1 | FEMALE) + (1 | TANK) + (1 | LEVEL) + (1 | POPULATION)
## Data: growth3 (Number of observations: 1961)
## Draws: 2 chains, each with iter = 5000; warmup = 500; thin = 5;
## total post-warmup draws = 1800
##
## Group-Level Effects:
## ~FEMALE (Number of levels: 15)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.02 0.02 0.00 0.06 1.00 925 1402
##
## ~LEVEL (Number of levels: 3)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.45 0.85 0.50 3.66 1.00 1193 1542
##
## ~POPULATION (Number of levels: 8)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.05 0.03 0.00 0.12 1.00 1170 1377
##
## ~TANK (Number of levels: 111)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.08 0.01 0.07 0.10 1.00 1491 1565
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 0.98 0.21 0.57 1.38 1.00
## DEV_TEMP30 0.05 0.03 -0.01 0.10 1.00
## DEV_TEMP31.5 0.07 0.03 0.01 0.12 1.00
## REGIONleading 0.03 0.05 -0.07 0.13 1.00
## scaleDENSITYcenterEQTRUEscaleEQTRUE -0.02 0.01 -0.04 -0.00 1.00
## scaleLENGTHcenterEQTRUEscaleEQTRUE 0.40 0.00 0.39 0.41 1.00
## DEV_TEMP30:REGIONleading -0.03 0.04 -0.11 0.05 1.00
## DEV_TEMP31.5:REGIONleading -0.03 0.04 -0.10 0.05 1.00
## Bulk_ESS Tail_ESS
## Intercept 1656 1524
## DEV_TEMP30 1305 1631
## DEV_TEMP31.5 1188 1361
## REGIONleading 1341 1528
## scaleDENSITYcenterEQTRUEscaleEQTRUE 1603 1667
## scaleLENGTHcenterEQTRUEscaleEQTRUE 1792 1828
## DEV_TEMP30:REGIONleading 1247 1504
## DEV_TEMP31.5:REGIONleading 1223 1451
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 41.21 1.34 38.64 43.82 1.00 1640 1869
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#model1.re.wo |> get_variables()
model3.1_gamma1 |> gather_draws(`b_.*|sigma`, regex =TRUE) |>
median_hdci()model3.1_gamma1 |> emmeans(pairwise ~ REGION*DEV_TEMP, type="response") |> pairs(by="DEV_TEMP") |> summary(infer=TRUE)model3.1_gamma1 |> emmeans(pairwise ~ REGION*DEV_TEMP, type="response") |> pairs(by="REGION") |> confint()## REGION DEV_TEMP response lower.HPD upper.HPD
## core 28.5 2.68 1.62 3.79
## leading 28.5 2.77 1.74 3.93
## core 30 2.81 1.69 3.95
## leading 30 2.83 1.76 4.00
## core 31.5 2.86 1.82 4.12
## leading 31.5 2.87 1.76 4.05
##
## Point estimate displayed: median
## HPD interval probability: 0.95
#model1.geo.gamma |> emmeans(~ REGION | DEV_TEMP, at = list(DEV_TEMP = 31.5, length.out = 10)) |> pairs(type = 'response')
mtsqst <- model3.1_gamma1 |> emmeans(pairwise ~ REGION*DEV_TEMP)
mtsqrt2 <- mtsqst$contrasts |> gather_emmeans_draws()
mtsqrt2 %>% group_by(contrast) %>% dplyr::summarise(Prob = sum(.value<0)/n())var <- get_variables(model3.1_gamma1)
var1 <- get_variables(model3.1_gamma1)[c(1:4,7,8)]
int_draws_spread <- model3.1_gamma1 |> spread_draws(!!!syms(var1))
int_draws_spread2 <- int_draws_spread |>
gather_draws(b_Intercept, b_REGIONleading) |>
left_join(int_draws_spread, by = c(".chain",".iteration",".draw"))
int_draws <- int_draws_spread2 |>
mutate(x28.5 = case_when(`.variable` == 'b_Intercept' ~
`.value`,
`.variable` != 'b_Intercept' ~
`.value` + b_Intercept),
x30 = case_when(`.variable` == 'b_Intercept' ~
`.value` + b_DEV_TEMP30,
`.variable` == 'b_REGIONleading' ~
`.value` + b_Intercept + b_DEV_TEMP30 + `b_DEV_TEMP30:REGIONleading`),
x31.5 = case_when(`.variable` == 'b_Intercept' ~
`.value` + b_DEV_TEMP31.5,
`.variable` == 'b_REGIONleading' ~
`.value` + b_Intercept + b_DEV_TEMP31.5 + `b_DEV_TEMP31.5:REGIONleading`))
int_draws_plotting <- int_draws |>
pivot_longer(cols = starts_with("x"),
names_to = "DEV_TEMP",
values_to = "MASS") |>
transmute(LATITUDE = case_when(`.variable` == "b_Intercept" ~ "Low latitude",
`.variable` == "b_REGIONleading" ~ "High latitude"),
DEV_TEMP = case_when(DEV_TEMP == 'x28.5' ~ 'DEV_TEMP_28.5',
DEV_TEMP == 'x30' ~ 'DEV_TEMP_30',
DEV_TEMP == 'x31.5' ~ 'DEV_TEMP_31.5'),
MASS = MASS,
LATITUDE_B = LATITUDE,
DEV_TEMP_B = DEV_TEMP,
chain = `.chain`,
iteration = `.iteration`,
draw_n = `.draw`) |>
unite("EXP_GROUP",LATITUDE_B, DEV_TEMP_B,sep="_") |>
mutate(EXP_GROUP = as.factor(EXP_GROUP)) |>
mutate(EXP_GROUP = factor(EXP_GROUP, levels=c("High latitude_DEV_TEMP_28.5","High latitude_DEV_TEMP_30", "High latitude_DEV_TEMP_31.5",
"Low latitude_DEV_TEMP_28.5","Low latitude_DEV_TEMP_30", "Low latitude_DEV_TEMP_31.5")))
mass.plot <- int_draws_plotting |>
ggplot(aes(x=EXP_GROUP, y=MASS)) +
#geom_hline(yintercept = 0, linetype="dashed", linewidth=1, color="grey58", alpha=0.8) +
stat_halfeye(aes(fill = EXP_GROUP, fill_ramp = after_stat(level)),
point_interval = median_hdci,
.width = c(.66, .89, .95)) +
scale_fill_ramp_discrete(na.translate=FALSE,
labels =c("0.95","0.89","0.66"),
name = "Credible interval") +
scale_fill_manual(values = c("lightskyblue" ,"dodgerblue2", "dodgerblue4","coral", "red2","firebrick4"))+
scale_y_continuous(limits=c(0,2), breaks = seq(0,2, .5))+
ylab("MASS (g)") + xlab("EXPERIMENTAL GROUP") +
scale_x_discrete(labels = c("Low latitude_DEV_TEMP_28.5" = paste0("Low latitude 28.5","\u00B0","C"),
"Low latitude_DEV_TEMP_30" = paste0("Low latitude 30","\u00B0","C"),
"Low latitude_DEV_TEMP_31.5" = paste0("Low latitude 31.5","\u00B0","C"),
"High latitude_DEV_TEMP_28.5" = paste0("High latitude 28.5","\u00B0","C"),
"High latitude_DEV_TEMP_30" = paste0("High latitude 30","\u00B0","C"),
"High latitude_DEV_TEMP_31.5" = paste0("High latitude 31.5","\u00B0","C"))) +
#annotate("text", x=6.8,y=1.4, label = paste0(round(mean(growth3$MASS), 2)," (mm)"), color="grey58") +
coord_flip() +
theme_classic() +
guides(fill = "none") +
theme(legend.position = c(.15,.86),
axis.title.y = element_text(margin = margin(r =0.3, unit = "in"), size = 12),
axis.title.x = element_text(margin = margin(t = 0.3, unit="in"), size =12),
legend.key = element_rect(color="black", size=1.25),
legend.background = element_rect(fill = alpha("blue", 0))); mass.plotmodel_gamma.priors <- prior(normal(1.13, 0.20), class="Intercept") +
prior(normal(0, 0.25), class="b")f.model3.1.nolength <- bf(MASS ~ 1 +
DEV_TEMP*REGION +
scale(DENSITY, center=TRUE, scale=TRUE) +
#scale(AGE_DAYS, center=TRUE, scale=TRUE) +
#scale(LENGTH, center=TRUE, scale=TRUE) +
(1| FEMALE) + (1| TANK) + (1|LEVEL) + (1| POPULATION),
family=Gamma(link = "log"))
model3.1.nolength <- brm(f.model3.1.nolength,
data = growth3,
prior = model_gamma.priors,
warmup = 500,
iter = 5000,
seed=123,
cores=2,
sample_prior = "yes",
save_pars = save_pars(all=TRUE),
chains = 2,
thin = 5,
control = list(adapt_delta=0.95)) ## Compiling Stan program...
## Start sampling
## Warning: There were 2 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: There were 71 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: Examine the pairs() plot to diagnose sampling problems
var <- get_variables(model3.1.nolength)
var1 <- get_variables(model3.1.nolength)[c(1:4,6,7)]
int_draws_spread <- model3.1.nolength |> spread_draws(!!!syms(var1))
int_draws_spread2 <- int_draws_spread |>
gather_draws(b_Intercept, b_REGIONleading) |>
left_join(int_draws_spread, by = c(".chain",".iteration",".draw"))
int_draws <- int_draws_spread2 |>
mutate(x28.5 = case_when(`.variable` == 'b_Intercept' ~
`.value`,
`.variable` != 'b_Intercept' ~
`.value` + b_Intercept),
x30 = case_when(`.variable` == 'b_Intercept' ~
`.value` + b_DEV_TEMP30,
`.variable` == 'b_REGIONleading' ~
`.value` + b_Intercept + b_DEV_TEMP30 + `b_DEV_TEMP30:REGIONleading`),
x31.5 = case_when(`.variable` == 'b_Intercept' ~
`.value` + b_DEV_TEMP31.5,
`.variable` == 'b_REGIONleading' ~
`.value` + b_Intercept + b_DEV_TEMP31.5 + `b_DEV_TEMP31.5:REGIONleading`))
int_draws_plotting <- int_draws |>
pivot_longer(cols = starts_with("x"),
names_to = "DEV_TEMP",
values_to = "MASS") |>
transmute(LATITUDE = case_when(`.variable` == "b_Intercept" ~ "Low latitude",
`.variable` == "b_REGIONleading" ~ "High latitude"),
DEV_TEMP = case_when(DEV_TEMP == 'x28.5' ~ 'DEV_TEMP_28.5',
DEV_TEMP == 'x30' ~ 'DEV_TEMP_30',
DEV_TEMP == 'x31.5' ~ 'DEV_TEMP_31.5'),
MASS = MASS,
LATITUDE_B = LATITUDE,
DEV_TEMP_B = DEV_TEMP,
chain = `.chain`,
iteration = `.iteration`,
draw_n = `.draw`) |>
unite("EXP_GROUP",LATITUDE_B, DEV_TEMP_B,sep="_") |>
mutate(EXP_GROUP = as.factor(EXP_GROUP)) |>
mutate(EXP_GROUP = factor(EXP_GROUP, levels=c("High latitude_DEV_TEMP_28.5","High latitude_DEV_TEMP_30", "High latitude_DEV_TEMP_31.5",
"Low latitude_DEV_TEMP_28.5","Low latitude_DEV_TEMP_30", "Low latitude_DEV_TEMP_31.5")))
mass.plot <- int_draws_plotting |>
ggplot(aes(x=EXP_GROUP, y=MASS)) +
#geom_hline(yintercept = 0, linetype="dashed", linewidth=1, color="grey58", alpha=0.8) +
stat_halfeye(aes(fill = EXP_GROUP, fill_ramp = after_stat(level)),
point_interval = median_hdci,
.width = c(.66, .89, .95)) +
scale_fill_ramp_discrete(na.translate=FALSE,
labels =c("0.95","0.89","0.66"),
name = "Credible interval") +
scale_fill_manual(values = c("lightskyblue" ,"dodgerblue2", "dodgerblue4","coral", "red2","firebrick4"))+
scale_y_continuous(limits=c(0,2), breaks = seq(0,2, .5))+
ylab("MASS (g)") + xlab("EXPERIMENTAL GROUP") +
scale_x_discrete(labels = c("Low latitude_DEV_TEMP_28.5" = paste0("Low latitude 28.5","\u00B0","C"),
"Low latitude_DEV_TEMP_30" = paste0("Low latitude 30","\u00B0","C"),
"Low latitude_DEV_TEMP_31.5" = paste0("Low latitude 31.5","\u00B0","C"),
"High latitude_DEV_TEMP_28.5" = paste0("High latitude 28.5","\u00B0","C"),
"High latitude_DEV_TEMP_30" = paste0("High latitude 30","\u00B0","C"),
"High latitude_DEV_TEMP_31.5" = paste0("High latitude 31.5","\u00B0","C"))) +
#annotate("text", x=6.8,y=1.4, label = paste0(round(mean(growth3$MASS), 2)," (mm)"), color="grey58") +
coord_flip() +
theme_classic() +
guides(fill = "none") +
theme(legend.position = c(.15,.86),
axis.title.y = element_text(margin = margin(r =0.3, unit = "in"), size = 12),
axis.title.x = element_text(margin = margin(t = 0.3, unit="in"), size =12),
legend.key = element_rect(color="black", size=1.25),
legend.background = element_rect(fill = alpha("blue", 0))); mass.plot